Abstract
Geometric inversion is applied to two-dimensional Stokes flow in view to find new Stokes flow solutions. The principle of this method and the relations between the reference and inverse fluid velocity fields are presented. They are followed by applications to the flow between two parallel plates induced by a rotating or a translating cylinder. Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are thus deduced. Typically fluid flow patterns around two circular cylinders in contact placed in the centre of a rotating or a translating circular cylinder are illustrated.
Highlights
Geometric inversion is a type of transformation of the Euclidean plane
Geometric inversion is applied to two-dimensional Stokes flow in view to find new Stokes flow solutions
In fluid mechanics, the equation of two-dimensional Stokes flow remains valid in the new coordinates system obtained by inversion
Summary
Geometric inversion is a type of transformation of the Euclidean plane. This transformation preserves angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (a circle with infinite radius). Two-dimensional Stokes flow around certain bodies presenting circular shape appears less difficult to calculate by inversion of flow in channels of parallel walls than by direct calculation using polar coordinates. This method is rather general, we will apply it to the case of cellular flows (recirculation flow) presenting viscous eddies. Several theoretical and numerical results are available They could be useful to obtain by inversion transformation the structure and the features of Stokes flows around bodies of circular shape. This transformation is useful to obtain flow around bodies with complex shape for which the direct calculation could be tiresome
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